LMFDB - Embedded newform 25.34.b.d.24.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,Mod(24,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 34, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$172.457072203$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.11
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-642.905i q^{2} +5.85306e7i q^{3} +8.58952e9 q^{4} +3.76296e10 q^{6} +1.03914e14i q^{7} -1.10448e13i q^{8} +2.13323e15 q^{9} +O(q^{10})$	\(q-642.905i q^{2} +5.85306e7i q^{3} +8.58952e9 q^{4} +3.76296e10 q^{6} +1.03914e14i q^{7} -1.10448e13i q^{8} +2.13323e15 q^{9} -4.04723e16 q^{11} +5.02750e17i q^{12} +3.61885e18i q^{13} +6.68070e16 q^{14} +7.37763e19 q^{16} +2.12343e20i q^{17} -1.37147e18i q^{18} +6.69296e20 q^{19} -6.08216e21 q^{21} +2.60199e19i q^{22} -4.58890e21i q^{23} +6.46456e20 q^{24} +2.32658e21 q^{26} +4.50234e23i q^{27} +8.92574e23i q^{28} +2.08845e24 q^{29} -2.71951e24 q^{31} -1.42305e23i q^{32} -2.36887e24i q^{33} +1.36516e23 q^{34} +1.83234e25 q^{36} +2.98538e25i q^{37} -4.30294e23i q^{38} -2.11813e26 q^{39} -2.01426e26 q^{41} +3.91025e24i q^{42} -9.42876e26i q^{43} -3.47638e26 q^{44} -2.95023e24 q^{46} +4.81286e27i q^{47} +4.31817e27i q^{48} -3.06719e27 q^{49} -1.24286e28 q^{51} +3.10842e28i q^{52} -1.34565e28i q^{53} +2.89458e26 q^{54} +1.14771e27 q^{56} +3.91743e28i q^{57} -1.34267e27i q^{58} -3.17580e29 q^{59} +4.25546e29 q^{61} +1.74839e27i q^{62} +2.21673e29i q^{63} +6.33642e29 q^{64} -1.52296e27 q^{66} +3.16821e29i q^{67} +1.82392e30i q^{68} +2.68591e29 q^{69} +5.91891e30 q^{71} -2.35610e28i q^{72} +2.98266e30i q^{73} +1.91932e28 q^{74} +5.74893e30 q^{76} -4.20565e30i q^{77} +1.36176e29i q^{78} -4.21980e30 q^{79} -1.44937e31 q^{81} +1.29498e29i q^{82} -2.51439e31i q^{83} -5.22429e31 q^{84} -6.06179e29 q^{86} +1.22238e32i q^{87} +4.47007e29i q^{88} +1.35942e32 q^{89} -3.76050e32 q^{91} -3.94165e31i q^{92} -1.59175e32i q^{93} +3.09421e30 q^{94} +8.32918e30 q^{96} -7.72579e32i q^{97} +1.97191e30i q^{98} -8.63369e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 642.905i	− 0.00693668i	−0.999994	−	0.00346834i	$-0.998896\pi$
$2$	− 642.905i	− 0.00693668i	0.999994	−	0.00346834i	$-0.00110401\pi$
$3$	5.85306e7i	0.785022i	0.919747	+	0.392511i	$0.128394\pi$
$3$	5.85306e7i	0.785022i	−0.919747	+	0.392511i	$0.871606\pi$
$4$	8.58952e9	0.999952
$5$	0	0
$5$	0	0
$6$	3.76296e10	0.00544545
$7$	1.03914e14i	1.18184i	0.806731	+	0.590919i	$0.201235\pi$
$7$	1.03914e14i	1.18184i	−0.806731	+	0.590919i	$0.798765\pi$
$8$	− 1.10448e13i	− 0.0138730i
$9$	2.13323e15	0.383740
$10$	0	0
$11$	−4.04723e16	−0.265570	−0.132785	−	0.991145i	$-0.542392\pi$
$11$	−4.04723e16	−0.265570	−0.132785	+	0.991145i	$0.542392\pi$
$12$	5.02750e17i	0.784985i
$13$	3.61885e18i	1.50836i	0.656667	+	0.754181i	$0.271966\pi$
$13$	3.61885e18i	1.50836i	−0.656667	+	0.754181i	$0.728034\pi$
$14$	6.68070e16	0.00819803
$15$	0	0
$16$	7.37763e19	0.999856
$17$	2.12343e20i	1.05835i	0.848512	+	0.529176i	$0.177499\pi$
$17$	2.12343e20i	1.05835i	−0.848512	+	0.529176i	$0.822501\pi$
$18$	− 1.37147e18i	− 0.00266188i
$19$	6.69296e20	0.532334	0.266167	−	0.963927i	$-0.414243\pi$
$19$	6.69296e20	0.532334	0.266167	+	0.963927i	$0.414243\pi$
$20$	0	0
$21$	−6.08216e21	−0.927769
$22$	2.60199e19i	0.00184217i
$23$	− 4.58890e21i	− 0.156027i	−0.996952	−	0.0780134i	$-0.975142\pi$
$23$	− 4.58890e21i	− 0.156027i	0.996952	−	0.0780134i	$-0.0248577\pi$
$24$	6.46456e20	0.0108906
$25$	0	0
$26$	2.32658e21	0.0104630
$27$	4.50234e23i	1.08627i
$28$	8.92574e23i	1.18178i
$29$	2.08845e24	1.54973	0.774866	−	0.632125i	$-0.217817\pi$
$29$	2.08845e24	1.54973	0.774866	+	0.632125i	$0.217817\pi$
$30$	0	0
$31$	−2.71951e24	−0.671465	−0.335732	−	0.941957i	$-0.608984\pi$
$31$	−2.71951e24	−0.671465	−0.335732	+	0.941957i	$0.608984\pi$
$32$	− 1.42305e23i	− 0.0208087i
$33$	− 2.36887e24i	− 0.208478i
$34$	1.36516e23	0.00734146
$35$	0	0
$36$	1.83234e25	0.383721
$37$	2.98538e25i	0.397806i	0.980019	+	0.198903i	$0.0637379\pi$
$37$	2.98538e25i	0.397806i	−0.980019	+	0.198903i	$0.936262\pi$
$38$	− 4.30294e23i	− 0.00369263i
$39$	−2.11813e26	−1.18410
$40$	0	0
$41$	−2.01426e26	−0.493380	−0.246690	−	0.969094i	$-0.579343\pi$
$41$	−2.01426e26	−0.493380	−0.246690	+	0.969094i	$0.579343\pi$
$42$	3.91025e24i	0.00643563i
$43$	− 9.42876e26i	− 1.05251i	−0.850328	−	0.526254i	$-0.823596\pi$
$43$	− 9.42876e26i	− 1.05251i	0.850328	−	0.526254i	$-0.176404\pi$
$44$	−3.47638e26	−0.265557
$45$	0	0
$46$	−2.95023e24	−0.00108231
$47$	4.81286e27i	1.23819i	0.785315	+	0.619097i	$0.212501\pi$
$47$	4.81286e27i	1.23819i	−0.785315	+	0.619097i	$0.787499\pi$
$48$	4.31817e27i	0.784909i
$49$	−3.06719e27	−0.396739
$50$	0	0
$51$	−1.24286e28	−0.830831
$52$	3.10842e28i	1.50829i
$53$	− 1.34565e28i	− 0.476850i	−0.971161	−	0.238425i	$-0.923369\pi$
$53$	− 1.34565e28i	− 0.476850i	0.971161	−	0.238425i	$-0.0766311\pi$
$54$	2.89458e26	0.00753509
$55$	0	0
$56$	1.14771e27	0.0163957
$57$	3.91743e28i	0.417894i
$58$	− 1.34267e27i	− 0.0107500i
$59$	−3.17580e29	−1.91776	−0.958880	−	0.283812i	$-0.908401\pi$
$59$	−3.17580e29	−1.91776	−0.958880	+	0.283812i	$0.908401\pi$
$60$	0	0
$61$	4.25546e29	1.48253	0.741266	−	0.671211i	$-0.234225\pi$
$61$	4.25546e29	1.48253	0.741266	+	0.671211i	$0.234225\pi$
$62$	1.74839e27i	0.00465774i
$63$	2.21673e29i	0.453518i
$64$	6.33642e29	0.999711
$65$	0	0
$66$	−1.52296e27	−0.00144615
$67$	3.16821e29i	0.234736i	0.993088	+	0.117368i	$0.0374457\pi$
$67$	3.16821e29i	0.234736i	−0.993088	+	0.117368i	$0.962554\pi$
$68$	1.82392e30i	1.05830i
$69$	2.68591e29	0.122485
$70$	0	0
$71$	5.91891e30	1.68453	0.842266	−	0.539062i	$-0.181221\pi$
$71$	5.91891e30	1.68453	0.842266	+	0.539062i	$0.181221\pi$
$72$	− 2.35610e28i	− 0.00532363i
$73$	2.98266e30i	0.536756i	0.963314	+	0.268378i	$0.0864876\pi$
$73$	2.98266e30i	0.536756i	−0.963314	+	0.268378i	$0.913512\pi$
$74$	1.91932e28	0.00275945
$75$	0	0
$76$	5.74893e30	0.532308
$77$	− 4.20565e30i	− 0.313860i
$78$	1.36176e29i	0.00821371i
$79$	−4.21980e30	−0.206274	−0.103137	−	0.994667i	$-0.532888\pi$
$79$	−4.21980e30	−0.206274	−0.103137	+	0.994667i	$0.532888\pi$
$80$	0	0
$81$	−1.44937e31	−0.469004
$82$	1.29498e29i	0.00342242i
$83$	− 2.51439e31i	− 0.544057i	−0.962289	−	0.272029i	$-0.912305\pi$
$83$	− 2.51439e31i	− 0.544057i	0.962289	−	0.272029i	$-0.0876945\pi$
$84$	−5.22429e31	−0.927724
$85$	0	0
$86$	−6.06179e29	−0.00730090
$87$	1.22238e32i	1.21657i
$88$	4.47007e29i	0.00368426i
$89$	1.35942e32	0.929859	0.464930	−	0.885348i	$-0.346080\pi$
$89$	1.35942e32	0.929859	0.464930	+	0.885348i	$0.346080\pi$
$90$	0	0
$91$	−3.76050e32	−1.78264
$92$	− 3.94165e31i	− 0.156019i
$93$	− 1.59175e32i	− 0.527115i
$94$	3.09421e30	0.00858895
$95$	0	0
$96$	8.32918e30	0.0163353
$97$	− 7.72579e32i	− 1.27705i	−0.769599	−	0.638527i	$-0.779544\pi$
$97$	− 7.72579e32i	− 1.27705i	0.769599	−	0.638527i	$-0.220456\pi$
$98$	1.97191e30i	0.00275205i
$99$	−8.63369e31	−0.101910
$100$	0	0
$101$	8.12814e32	0.689745	0.344873	−	0.938650i	$-0.387922\pi$
$101$	8.12814e32	0.689745	0.344873	+	0.938650i	$0.387922\pi$
$102$	7.99037e30i	0.00576321i
$103$	− 9.66587e32i	− 0.593508i	−0.954954	−	0.296754i	$-0.904096\pi$
$103$	− 9.66587e32i	− 0.593508i	0.954954	−	0.296754i	$-0.0959041\pi$
$104$	3.99693e31	0.0209255
$105$	0	0
$106$	−8.65128e30	−0.00330776
$107$	− 2.85497e33i	− 0.934910i	−0.884017	−	0.467455i	$-0.845171\pi$
$107$	− 2.85497e33i	− 0.934910i	0.884017	−	0.467455i	$-0.154829\pi$
$108$	3.86730e33i	1.08621i
$109$	2.85246e33	0.688149	0.344074	−	0.938942i	$-0.388193\pi$
$109$	2.85246e33	0.688149	0.344074	+	0.938942i	$0.388193\pi$
$110$	0	0
$111$	−1.74736e33	−0.312287
$112$	7.66641e33i	1.18167i
$113$	1.89710e33i	0.252520i	0.991997	+	0.126260i	$0.0402973\pi$
$113$	1.89710e33i	0.252520i	−0.991997	+	0.126260i	$0.959703\pi$
$114$	2.51853e31	0.00289880
$115$	0	0
$116$	1.79388e34	1.54966
$117$	7.71985e33i	0.578818i
$118$	2.04173e32i	0.0133029i
$119$	−2.20655e34	−1.25080
$120$	0	0
$121$	−2.15871e34	−0.929473
$122$	− 2.73586e32i	− 0.0102839i
$123$	− 1.17896e34i	− 0.387314i
$124$	−2.33593e34	−0.671432
$125$	0	0
$126$	1.42515e32	0.00314591
$127$	2.09944e34i	0.406764i	0.979099	+	0.203382i	$0.0651934\pi$
$127$	2.09944e34i	0.406764i	−0.979099	+	0.203382i	$0.934807\pi$
$128$	− 1.62976e33i	− 0.0277434i
$129$	5.51871e34	0.826242
$130$	0	0
$131$	−9.99620e33	−0.116107	−0.0580535	−	0.998313i	$-0.518489\pi$
$131$	−9.99620e33	−0.116107	−0.0580535	+	0.998313i	$0.518489\pi$
$132$	− 2.03475e34i	− 0.208468i
$133$	6.95494e34i	0.629132i
$134$	2.03686e32	0.00162829
$135$	0	0
$136$	2.34527e33	0.0146826
$137$	− 2.62787e35i	− 1.45786i	−0.684589	−	0.728929i	$-0.740018\pi$
$137$	− 2.62787e35i	− 1.45786i	0.684589	−	0.728929i	$-0.259982\pi$
$138$	− 1.72678e32i	0 0.000849636i
$139$	1.85064e35	0.808310	0.404155	−	0.914691i	$-0.367566\pi$
$139$	1.85064e35	0.808310	0.404155	+	0.914691i	$0.367566\pi$
$140$	0	0
$141$	−2.81699e35	−0.972010
$142$	− 3.80530e33i	− 0.0116851i
$143$	− 1.46463e35i	− 0.400576i
$144$	1.57382e35	0.383684
$145$	0	0
$146$	1.91757e33	0.00372331
$147$	− 1.79524e35i	− 0.311449i
$148$	2.56430e35i	0.397787i
$149$	−1.40401e36	−1.94893	−0.974466	−	0.224533i	$-0.927914\pi$
$149$	−1.40401e36	−1.94893	−0.974466	+	0.224533i	$0.927914\pi$
$150$	0	0
$151$	5.76801e35	0.642549	0.321274	−	0.946986i	$-0.395889\pi$
$151$	5.76801e35	0.642549	0.321274	+	0.946986i	$0.395889\pi$
$152$	− 7.39221e33i	− 0.00738508i
$153$	4.52977e35i	0.406132i
$154$	−2.70383e33	−0.00217715
$155$	0	0
$156$	−1.81938e36	−1.18404
$157$	2.11922e36i	1.24117i	0.784138	+	0.620586i	$0.213105\pi$
$157$	2.11922e36i	1.24117i	−0.784138	+	0.620586i	$0.786895\pi$
$158$	2.71293e33i	0.00143086i
$159$	7.87620e35	0.374338
$160$	0	0
$161$	4.76852e35	0.184398
$162$	9.31807e33i	0.00325333i
$163$	5.64371e36i	1.78020i	0.455764	+	0.890101i	$0.349366\pi$
$163$	5.64371e36i	1.78020i	−0.455764	+	0.890101i	$0.650634\pi$
$164$	−1.73015e36	−0.493356
$165$	0	0
$166$	−1.61651e34	−0.00377395
$167$	3.22707e35i	0.0682317i	0.999418	+	0.0341159i	$0.0108615\pi$
$167$	3.22707e35i	0.0682317i	−0.999418	+	0.0341159i	$0.989138\pi$
$168$	6.71760e34i	0.0128710i
$169$	−7.33996e36	−1.27515
$170$	0	0
$171$	1.42776e36	0.204278
$172$	− 8.09885e36i	− 1.05246i
$173$	7.28030e36i	0.859782i	0.902881	+	0.429891i	$0.141448\pi$
$173$	7.28030e36i	0.859782i	−0.902881	+	0.429891i	$0.858552\pi$
$174$	7.85874e34	0.00843899
$175$	0	0
$176$	−2.98590e36	−0.265532
$177$	− 1.85881e37i	− 1.50548i
$178$	− 8.73975e34i	− 0.00645013i
$179$	3.91390e36	0.263351	0.131675	−	0.991293i	$-0.457964\pi$
$179$	3.91390e36	0.263351	0.131675	+	0.991293i	$0.457964\pi$
$180$	0	0
$181$	−2.82964e37	−1.58502	−0.792509	−	0.609860i	$-0.791226\pi$
$181$	−2.82964e37	−1.58502	−0.792509	+	0.609860i	$0.791226\pi$
$182$	2.41765e35i	0.0123656i
$183$	2.49075e37i	1.16382i
$184$	−5.06833e34	−0.00216456
$185$	0	0
$186$	−1.02334e35	−0.00365643
$187$	− 8.59401e36i	− 0.281067i
$188$	4.13402e37i	1.23813i
$189$	−4.67858e37	−1.28379
$190$	0	0
$191$	−8.41989e37	−1.94203	−0.971015	−	0.239017i	$-0.923175\pi$
$191$	−8.41989e37	−1.94203	−0.971015	+	0.239017i	$0.923175\pi$
$192$	3.70874e37i	0.784796i
$193$	1.21898e37i	0.236755i	0.992969	+	0.118378i	$0.0377693\pi$
$193$	1.21898e37i	0.236755i	−0.992969	+	0.118378i	$0.962231\pi$
$194$	−4.96695e35	−0.00885852
$195$	0	0
$196$	−2.63457e37	−0.396720
$197$	− 7.93299e37i	− 1.09836i	−0.835704	−	0.549180i	$-0.814940\pi$
$197$	− 7.93299e37i	− 1.09836i	0.835704	−	0.549180i	$-0.185060\pi$
$198$	5.55064e34i	0 0.000706915i
$199$	−1.43151e38	−1.67772	−0.838860	−	0.544348i	$-0.816777\pi$
$199$	−1.43151e38	−1.67772	−0.838860	+	0.544348i	$0.816777\pi$
$200$	0	0
$201$	−1.85437e37	−0.184273
$202$	− 5.22562e35i	− 0.00478454i
$203$	2.17020e38i	1.83153i
$204$	−1.06755e38	−0.830791
$205$	0	0
$206$	−6.21423e35	−0.00411698
$207$	− 9.78919e36i	− 0.0598737i
$208$	2.66986e38i	1.50814i
$209$	−2.70880e37	−0.141372
$210$	0	0
$211$	6.95232e35	0.00310077	0.00155038	−	0.999999i	$-0.499506\pi$
$211$	6.95232e35	0.00310077	0.00155038	+	0.999999i	$0.499506\pi$
$212$	− 1.15585e38i	− 0.476827i
$213$	3.46437e38i	1.32240i
$214$	−1.83548e36	−0.00648517
$215$	0	0
$216$	4.97273e36	0.0150698
$217$	− 2.82596e38i	− 0.793562i
$218$	− 1.83386e36i	− 0.00477347i
$219$	−1.74577e38	−0.421366
$220$	0	0
$221$	−7.68437e38	−1.59638
$222$	1.12339e36i	0.00216623i
$223$	8.42136e38i	1.50783i	0.656973	+	0.753914i	$0.271837\pi$
$223$	8.42136e38i	1.50783i	−0.656973	+	0.753914i	$0.728163\pi$
$224$	1.47875e37	0.0245925
$225$	0	0
$226$	1.21965e36	0.00175165
$227$	− 4.33859e38i	− 0.579324i	−0.957129	−	0.289662i	$-0.906457\pi$
$227$	− 4.33859e38i	− 0.579324i	0.957129	−	0.289662i	$-0.0935429\pi$
$228$	3.36488e38i	0.417874i
$229$	−1.01177e39	−1.16896	−0.584478	−	0.811410i	$-0.698701\pi$
$229$	−1.01177e39	−1.16896	−0.584478	+	0.811410i	$0.698701\pi$
$230$	0	0
$231$	2.46159e38	0.246388
$232$	− 2.30664e37i	− 0.0214995i
$233$	− 1.30327e39i	− 1.13151i	−0.824572	−	0.565757i	$-0.808584\pi$
$233$	− 1.30327e39i	− 1.13151i	0.824572	−	0.565757i	$-0.191416\pi$
$234$	4.96313e36	0.00401508
$235$	0	0
$236$	−2.72786e39	−1.91767
$237$	− 2.46988e38i	− 0.161930i
$238$	1.41860e37i	0.00867640i
$239$	−2.27541e39	−1.29865	−0.649327	−	0.760509i	$-0.724949\pi$
$239$	−2.27541e39	−1.29865	−0.649327	+	0.760509i	$0.724949\pi$
$240$	0	0
$241$	−7.73852e38	−0.384926	−0.192463	−	0.981304i	$-0.561647\pi$
$241$	−7.73852e38	−0.384926	−0.192463	+	0.981304i	$0.561647\pi$
$242$	1.38785e37i	0.00644745i
$243$	1.65455e39i	0.718088i
$244$	3.65524e39	1.48246
$245$	0	0
$246$	−7.57957e36	−0.00268668
$247$	2.42208e39i	0.802952i
$248$	3.00363e37i	0.00931525i
$249$	1.47169e39	0.427097
$250$	0	0
$251$	4.56085e39	1.15992	0.579962	−	0.814644i	$-0.303067\pi$
$251$	4.56085e39	1.15992	0.579962	+	0.814644i	$0.303067\pi$
$252$	1.90407e39i	0.453496i
$253$	1.85724e38i	0.0414360i
$254$	1.34974e37	0.00282160
$255$	0	0
$256$	5.44190e39	0.999519
$257$	− 8.75106e39i	− 1.50718i	−0.657347	−	0.753588i	$-0.728321\pi$
$257$	− 8.75106e39i	− 1.50718i	0.657347	−	0.753588i	$-0.271679\pi$
$258$	− 3.54800e37i	− 0.00573137i
$259$	−3.10224e39	−0.470142
$260$	0	0
$261$	4.45515e39	0.594694
$262$	6.42660e36i	0 0.000805397i
$263$	− 1.10339e40i	− 1.29855i	−0.760555	−	0.649273i	$-0.775073\pi$
$263$	− 1.10339e40i	− 1.29855i	0.760555	−	0.649273i	$-0.224927\pi$
$264$	−2.61636e37	−0.00289223
$265$	0	0
$266$	4.47137e37	0.00436409
$267$	7.95674e39i	0.729960i
$268$	2.72134e39i	0.234725i
$269$	1.84619e40	1.49749	0.748745	−	0.662858i	$-0.230657\pi$
$269$	1.84619e40	1.49749	0.748745	+	0.662858i	$0.230657\pi$
$270$	0	0
$271$	1.48576e40	1.06649	0.533244	−	0.845962i	$-0.320973\pi$
$271$	1.48576e40	1.06649	0.533244	+	0.845962i	$0.320973\pi$
$272$	1.56659e40i	1.05820i
$273$	− 2.20104e40i	− 1.39941i
$274$	−1.68947e38	−0.0101127
$275$	0	0
$276$	2.30707e39	0.122479
$277$	1.63998e40i	0.820204i	0.912040	+	0.410102i	$0.134507\pi$
$277$	1.63998e40i	0.820204i	−0.912040	+	0.410102i	$0.865493\pi$
$278$	− 1.18979e38i	− 0.00560699i
$279$	−5.80135e39	−0.257668
$280$	0	0
$281$	−2.80874e40	−1.10881	−0.554406	−	0.832246i	$-0.687055\pi$
$281$	−2.80874e40	−1.10881	−0.554406	+	0.832246i	$0.687055\pi$
$282$	1.81106e38i	0.00674252i
$283$	− 5.30091e40i	− 1.86155i	−0.365595	−	0.930774i	$-0.619135\pi$
$283$	− 5.30091e40i	− 1.86155i	0.365595	−	0.930774i	$-0.380865\pi$
$284$	5.08406e40	1.68445
$285$	0	0
$286$	−9.41620e37	−0.00277866
$287$	− 2.09310e40i	− 0.583095i
$288$	− 3.03569e38i	− 0.00798513i
$289$	−4.83501e39	−0.120111
$290$	0	0
$291$	4.52195e40	1.00252
$292$	2.56196e40i	0.536730i
$293$	− 9.02974e40i	− 1.78797i	−0.448100	−	0.893984i	$-0.647899\pi$
$293$	− 9.02974e40i	− 1.78797i	0.448100	−	0.893984i	$-0.352101\pi$
$294$	−1.15417e38	−0.00216042
$295$	0	0
$296$	3.29728e38	0.00551878
$297$	− 1.82220e40i	− 0.288480i
$298$	9.02645e38i	0.0135191i
$299$	1.66065e40	0.235345
$300$	0	0
$301$	9.79783e40	1.24389
$302$	− 3.70828e38i	− 0.00445716i
$303$	4.75745e40i	0.541465i
$304$	4.93782e40	0.532257
$305$	0	0
$306$	2.91221e38	0.00281721
$307$	− 2.72894e40i	− 0.250156i	−0.992147	−	0.125078i	$-0.960082\pi$
$307$	− 2.72894e40i	− 0.250156i	0.992147	−	0.125078i	$-0.0399180\pi$
$308$	− 3.61246e40i	− 0.313845i
$309$	5.65749e40	0.465917
$310$	0	0
$311$	9.31751e39	0.0689848	0.0344924	−	0.999405i	$-0.489019\pi$
$311$	9.31751e39	0.0689848	0.0344924	+	0.999405i	$0.489019\pi$
$312$	2.33943e39i	0.0164270i
$313$	1.02687e41i	0.683963i	0.939707	+	0.341982i	$0.111098\pi$
$313$	1.02687e41i	0.683963i	−0.939707	+	0.341982i	$0.888902\pi$
$314$	1.36246e39	0.00860962
$315$	0	0
$316$	−3.62461e40	−0.206264
$317$	1.75249e41i	0.946623i	0.880895	+	0.473311i	$0.156941\pi$
$317$	1.75249e41i	0.946623i	−0.880895	+	0.473311i	$0.843059\pi$
$318$	− 5.06364e38i	− 0.00259666i
$319$	−8.45244e40	−0.411562
$320$	0	0
$321$	1.67103e41	0.733925
$322$	− 3.06571e38i	− 0.00127911i
$323$	1.42120e41i	0.563397i
$324$	−1.24494e41	−0.468982
$325$	0	0
$326$	3.62837e39	0.0123487
$327$	1.66956e41i	0.540212i
$328$	2.22470e39i	0.00684467i
$329$	−5.00125e41	−1.46334
$330$	0	0
$331$	−6.69187e41	−1.77168	−0.885841	−	0.463989i	$-0.846418\pi$
$331$	−6.69187e41	−1.77168	−0.885841	+	0.463989i	$0.846418\pi$
$332$	− 2.15974e41i	− 0.544031i
$333$	6.36852e40i	0.152654i
$334$	2.07470e38	0.000473302 0
$335$	0	0
$336$	−4.48720e41	−0.927635
$337$	− 5.57473e41i	− 1.09731i	−0.836048	−	0.548656i	$-0.815140\pi$
$337$	− 5.57473e41i	− 1.09731i	0.836048	−	0.548656i	$-0.184860\pi$
$338$	4.71889e39i	0.00884534i
$339$	−1.11038e41	−0.198234
$340$	0	0
$341$	1.10065e41	0.178321
$342$	− 9.17916e38i	− 0.00141701i
$343$	4.84636e41i	0.712956i
$344$	−1.04138e40	−0.0146015
$345$	0	0
$346$	4.68054e39	0.00596403
$347$	− 5.73680e41i	− 0.697001i	−0.937309	−	0.348500i	$-0.886691\pi$
$347$	− 5.73680e41i	− 0.697001i	0.937309	−	0.348500i	$-0.113309\pi$
$348$	1.04997e42i	1.21652i
$349$	6.96962e41	0.770176	0.385088	−	0.922880i	$-0.374171\pi$
$349$	6.96962e41	0.770176	0.385088	+	0.922880i	$0.374171\pi$
$350$	0	0
$351$	−1.62933e42	−1.63848
$352$	5.75941e39i	0.00552617i
$353$	1.71218e42i	1.56772i	0.620941	+	0.783858i	$0.286751\pi$
$353$	1.71218e42i	1.56772i	−0.620941	+	0.783858i	$0.713249\pi$
$354$	−1.19504e40	−0.0104431
$355$	0	0
$356$	1.16767e42	0.929814
$357$	− 1.29150e42i	− 0.981907i
$358$	− 2.51627e39i	− 0.00182678i
$359$	−6.40235e41	−0.443896	−0.221948	−	0.975059i	$-0.571241\pi$
$359$	−6.40235e41	−0.443896	−0.221948	+	0.975059i	$0.571241\pi$
$360$	0	0
$361$	−1.13281e42	−0.716621
$362$	1.81919e40i	0.0109948i
$363$	− 1.26351e42i	− 0.729657i
$364$	−3.23009e42	−1.78255
$365$	0	0
$366$	1.60131e40	0.00807306
$367$	2.44832e41i	0.117999i	0.998258	+	0.0589994i	$0.0187910\pi$
$367$	2.44832e41i	0.117999i	−0.998258	+	0.0589994i	$0.981209\pi$
$368$	− 3.38552e41i	− 0.156004i
$369$	−4.29688e41	−0.189329
$370$	0	0
$371$	1.39833e42	0.563559
$372$	− 1.36723e42i	− 0.527090i
$373$	5.34187e42i	1.97014i	0.172147	+	0.985071i	$0.444930\pi$
$373$	5.34187e42i	1.97014i	−0.172147	+	0.985071i	$0.555070\pi$
$374$	−5.52513e39	−0.00194967
$375$	0	0
$376$	5.31568e40	0.0171775
$377$	7.55778e42i	2.33756i
$378$	3.00788e40i	0.00890524i
$379$	−3.34915e41	−0.0949265	−0.0474632	−	0.998873i	$-0.515114\pi$
$379$	−3.34915e41	−0.0949265	−0.0474632	+	0.998873i	$0.515114\pi$
$380$	0	0
$381$	−1.22882e42	−0.319319
$382$	5.41319e40i	0.0134712i
$383$	− 1.22154e42i	− 0.291157i	−0.989347	−	0.145579i	$-0.953496\pi$
$383$	− 1.22154e42i	− 0.291157i	0.989347	−	0.145579i	$-0.0465043\pi$
$384$	9.53908e40	0.0217792
$385$	0	0
$386$	7.83685e39	0.00164229
$387$	− 2.01137e42i	− 0.403889i
$388$	− 6.63609e42i	− 1.27699i
$389$	7.03138e42	1.29680	0.648399	−	0.761301i	$-0.275439\pi$
$389$	7.03138e42	1.29680	0.648399	+	0.761301i	$0.275439\pi$
$390$	0	0
$391$	9.74420e41	0.165131
$392$	3.38763e40i	0.00550397i
$393$	− 5.85083e41i	− 0.0911466i
$394$	−5.10016e40	−0.00761897
$395$	0	0
$396$	−7.41593e41	−0.101905
$397$	− 4.57583e42i	− 0.603152i	−0.953442	−	0.301576i	$-0.902487\pi$
$397$	− 4.57583e42i	− 0.603152i	0.953442	−	0.301576i	$-0.0975127\pi$
$398$	9.20326e40i	0.0116378i
$399$	−4.07077e42	−0.493883
$400$	0	0
$401$	6.37629e42	0.712338	0.356169	−	0.934422i	$-0.384083\pi$
$401$	6.37629e42	0.712338	0.356169	+	0.934422i	$0.384083\pi$
$402$	1.19219e40i	0.00127824i
$403$	− 9.84151e42i	− 1.01281i
$404$	6.98168e42	0.689712
$405$	0	0
$406$	1.39523e41	0.0127047
$407$	− 1.20825e42i	− 0.105645i
$408$	1.37270e41i	0.0115261i
$409$	1.70899e43	1.37818	0.689088	−	0.724678i	$-0.258011\pi$
$409$	1.70899e43	1.37818	0.689088	+	0.724678i	$0.258011\pi$
$410$	0	0
$411$	1.53811e43	1.14445
$412$	− 8.30252e42i	− 0.593479i
$413$	− 3.30010e43i	− 2.26648i
$414$	−6.29352e39	−0.000415325 0
$415$	0	0
$416$	5.14980e41	0.0313871
$417$	1.08319e43i	0.634542i
$418$	1.74150e40i	0 0.000980651i
$419$	6.84932e42	0.370780	0.185390	−	0.982665i	$-0.440645\pi$
$419$	6.84932e42	0.370780	0.185390	+	0.982665i	$0.440645\pi$
$420$	0	0
$421$	−1.32258e43	−0.661861	−0.330930	−	0.943655i	$-0.607363\pi$
$421$	−1.32258e43	−0.661861	−0.330930	+	0.943655i	$0.607363\pi$
$422$	− 4.46968e38i	0 2.15090e-5i
$423$	1.02669e43i	0.475144i
$424$	−1.48624e41	−0.00661535
$425$	0	0
$426$	2.22726e41	0.00917304
$427$	4.42203e43i	1.75211i
$428$	− 2.45229e43i	− 0.934865i
$429$	8.57259e42	0.314461
$430$	0	0
$431$	3.28785e43	1.11696	0.558478	−	0.829519i	$-0.311385\pi$
$431$	3.28785e43	1.11696	0.558478	+	0.829519i	$0.311385\pi$
$432$	3.32166e43i	1.08611i
$433$	1.68338e43i	0.529824i	0.964273	+	0.264912i	$0.0853428\pi$
$433$	1.68338e43i	0.529824i	−0.964273	+	0.264912i	$0.914657\pi$
$434$	−1.81682e41	−0.00550468
$435$	0	0
$436$	2.45013e43	0.688116
$437$	− 3.07133e42i	− 0.0830583i
$438$	1.12236e41i	0.00292288i
$439$	−3.05836e43	−0.767050	−0.383525	−	0.923531i	$-0.625290\pi$
$439$	−3.05836e43	−0.767050	−0.383525	+	0.923531i	$0.625290\pi$
$440$	0	0
$441$	−6.54302e42	−0.152244
$442$	4.94032e41i	0.0110736i
$443$	− 8.21070e43i	− 1.77304i	−0.462690	−	0.886520i	$-0.653116\pi$
$443$	− 8.21070e43i	− 1.77304i	0.462690	−	0.886520i	$-0.346884\pi$
$444$	−1.50090e43	−0.312272
$445$	0	0
$446$	5.41413e41	0.0104593
$447$	− 8.21775e43i	− 1.52996i
$448$	6.58445e43i	1.18150i
$449$	4.67364e43	0.808334	0.404167	−	0.914685i	$-0.367561\pi$
$449$	4.67364e43	0.808334	0.404167	+	0.914685i	$0.367561\pi$
$450$	0	0
$451$	8.15217e42	0.131027
$452$	1.62951e43i	0.252507i
$453$	3.37605e43i	0.504415i
$454$	−2.78930e41	−0.00401859
$455$	0	0
$456$	4.32670e41	0.00579745
$457$	− 4.35799e43i	− 0.563208i	−0.959531	−	0.281604i	$-0.909134\pi$
$457$	− 4.35799e43i	− 0.563208i	0.959531	−	0.281604i	$-0.0908665\pi$
$458$	6.50474e41i	0.00810867i
$459$	−9.56041e43	−1.14965
$460$	0	0
$461$	−5.51173e43	−0.616911	−0.308456	−	0.951239i	$-0.599812\pi$
$461$	−5.51173e43	−0.616911	−0.308456	+	0.951239i	$0.599812\pi$
$462$	− 1.58257e41i	− 0.00170911i
$463$	7.61652e43i	0.793726i	0.917878	+	0.396863i	$0.129901\pi$
$463$	7.61652e43i	0.793726i	−0.917878	+	0.396863i	$0.870099\pi$
$464$	1.54078e44	1.54951
$465$	0	0
$466$	−8.37875e41	−0.00784895
$467$	− 5.66070e43i	− 0.511848i	−0.966697	−	0.255924i	$-0.917620\pi$
$467$	− 5.66070e43i	− 0.511848i	0.966697	−	0.255924i	$-0.0823797\pi$
$468$	6.63098e43i	0.578790i
$469$	−3.29223e43	−0.277420
$470$	0	0
$471$	−1.24039e44	−0.974348
$472$	3.50759e42i	0.0266051i
$473$	3.81604e43i	0.279514i
$474$	−1.58789e41	−0.00112326
$475$	0	0
$476$	−1.89532e44	−1.25074
$477$	− 2.87059e43i	− 0.182986i
$478$	1.46287e42i	0.00900835i
$479$	−1.53369e44	−0.912436	−0.456218	−	0.889868i	$-0.650796\pi$
$479$	−1.53369e44	−0.912436	−0.456218	+	0.889868i	$0.650796\pi$
$480$	0	0
$481$	−1.08037e44	−0.600036
$482$	4.97513e41i	0.00267011i
$483$	2.79104e43i	0.144757i
$484$	−1.85423e44	−0.929428
$485$	0	0
$486$	1.06372e42	0.00498115
$487$	− 1.56849e44i	− 0.709993i	−0.934868	−	0.354996i	$-0.884482\pi$
$487$	− 1.56849e44i	− 0.709993i	0.934868	−	0.354996i	$-0.115518\pi$
$488$	− 4.70005e42i	− 0.0205672i
$489$	−3.30330e44	−1.39750
$490$	0	0
$491$	2.66401e44	1.05364	0.526818	−	0.849978i	$-0.323385\pi$
$491$	2.66401e44	1.05364	0.526818	+	0.849978i	$0.323385\pi$
$492$	− 1.01267e44i	− 0.387296i
$493$	4.43467e44i	1.64016i
$494$	1.55717e42	0.00556982
$495$	0	0
$496$	−2.00636e44	−0.671368
$497$	6.15060e44i	1.99084i
$498$	− 9.46155e41i	− 0.00296264i
$499$	−3.44761e43	−0.104438	−0.0522190	−	0.998636i	$-0.516629\pi$
$499$	−3.44761e43	−0.104438	−0.0522190	+	0.998636i	$0.516629\pi$
$500$	0	0
$501$	−1.88882e43	−0.0535634
$502$	− 2.93219e42i	− 0.00804602i
$503$	1.97299e44i	0.523905i	0.965081	+	0.261952i	$0.0843663\pi$
$503$	1.97299e44i	0.523905i	−0.965081	+	0.261952i	$0.915634\pi$
$504$	2.44833e42	0.00629166
$505$	0	0
$506$	1.19403e41	0.000287429 0
$507$	− 4.29612e44i	− 1.00102i
$508$	1.80332e44i	0.406745i
$509$	5.99115e44	1.30818	0.654089	−	0.756417i	$-0.273052\pi$
$509$	5.99115e44	1.30818	0.654089	+	0.756417i	$0.273052\pi$
$510$	0	0
$511$	−3.09941e44	−0.634358
$512$	− 1.74982e43i	− 0.0346767i
$513$	3.01340e44i	0.578256i
$514$	−5.62610e42	−0.0104548
$515$	0	0
$516$	4.74030e44	0.826202
$517$	− 1.94788e44i	− 0.328827i
$518$	1.99444e42i	0.00326123i
$519$	−4.26120e44	−0.674948
$520$	0	0
$521$	9.20734e44	1.36871	0.684356	−	0.729148i	$-0.260084\pi$
$521$	9.20734e44	1.36871	0.684356	+	0.729148i	$0.260084\pi$
$522$	− 2.86423e42i	− 0.00412520i
$523$	− 8.50723e44i	− 1.18716i	−0.804774	−	0.593581i	$-0.797714\pi$
$523$	− 8.50723e44i	− 1.18716i	0.804774	−	0.593581i	$-0.202286\pi$
$524$	−8.58625e43	−0.116101
$525$	0	0
$526$	−7.09372e42	−0.00900760
$527$	− 5.77469e44i	− 0.710647i
$528$	− 1.74766e44i	− 0.208448i
$529$	8.43947e44	0.975656
$530$	0	0
$531$	−6.77471e44	−0.735921
$532$	5.97396e44i	0.629101i
$533$	− 7.28930e44i	− 0.744195i
$534$	5.11542e42	0.00506350
$535$	0	0
$536$	3.49921e42	0.00325650
$537$	2.29083e44i	0.206736i
$538$	− 1.18693e43i	− 0.0103876i
$539$	1.24136e44	0.105362
$540$	0	0
$541$	−1.15298e45	−0.920593	−0.460296	−	0.887765i	$-0.652257\pi$
$541$	−1.15298e45	−0.920593	−0.460296	+	0.887765i	$0.652257\pi$
$542$	− 9.55203e42i	− 0.00739788i
$543$	− 1.65620e45i	− 1.24427i
$544$	3.02174e43	0.0220230
$545$	0	0
$546$	−1.41506e43	−0.00970726
$547$	1.27201e45i	0.846638i	0.905981	+	0.423319i	$0.139135\pi$
$547$	1.27201e45i	0.846638i	−0.905981	+	0.423319i	$0.860865\pi$
$548$	− 2.25722e45i	− 1.45779i
$549$	9.07789e44	0.568907
$550$	0	0
$551$	1.39779e45	0.824975
$552$	− 2.96652e42i	− 0.00169923i
$553$	− 4.38498e44i	− 0.243783i
$554$	1.05435e43	0.00568949
$555$	0	0
$556$	1.58961e45	0.808271
$557$	3.03968e45i	1.50044i	0.661191	+	0.750218i	$0.270051\pi$
$557$	3.03968e45i	1.50044i	−0.661191	+	0.750218i	$0.729949\pi$
$558$	3.72972e42i	0.00178736i
$559$	3.41213e45	1.58756
$560$	0	0
$561$	5.03013e44	0.220644
$562$	1.80576e43i	0.00769148i
$563$	2.40727e45i	0.995716i	0.867259	+	0.497858i	$0.165880\pi$
$563$	2.40727e45i	0.995716i	−0.867259	+	0.497858i	$0.834120\pi$
$564$	−2.41966e45	−0.971963
$565$	0	0
$566$	−3.40798e43	−0.0129130
$567$	− 1.50610e45i	− 0.554286i
$568$	− 6.53729e43i	− 0.0233696i
$569$	1.67468e45	0.581539	0.290769	−	0.956793i	$-0.406089\pi$
$569$	1.67468e45	0.581539	0.290769	+	0.956793i	$0.406089\pi$
$570$	0	0
$571$	3.07822e45	1.00880	0.504399	−	0.863471i	$-0.331714\pi$
$571$	3.07822e45	1.00880	0.504399	+	0.863471i	$0.331714\pi$
$572$	− 1.25805e45i	− 0.400556i
$573$	− 4.92821e45i	− 1.52454i
$574$	−1.34567e43	−0.00404474
$575$	0	0
$576$	1.35171e45	0.383629
$577$	− 2.65106e45i	− 0.731169i	−0.930778	−	0.365585i	$-0.880869\pi$
$577$	− 2.65106e45i	− 0.731169i	0.930778	−	0.365585i	$-0.119131\pi$
$578$	3.10845e42i	0 0.000833172i
$579$	−7.13473e44	−0.185858
$580$	0	0
$581$	2.61281e45	0.642987
$582$	− 2.90718e43i	− 0.00695414i
$583$	5.44618e44i	0.126637i
$584$	3.29428e43	0.00744643
$585$	0	0
$586$	−5.80526e43	−0.0124026
$587$	5.61606e45i	1.16655i	0.812275	+	0.583274i	$0.198229\pi$
$587$	5.61606e45i	1.16655i	−0.812275	+	0.583274i	$0.801771\pi$
$588$	− 1.54203e45i	− 0.311434i
$589$	−1.82016e45	−0.357443
$590$	0	0
$591$	4.64323e45	0.862237
$592$	2.20251e45i	0.397749i
$593$	1.02970e46i	1.80845i	0.427056	+	0.904225i	$0.359551\pi$
$593$	1.02970e46i	1.80845i	−0.427056	+	0.904225i	$0.640449\pi$
$594$	−1.17150e43	−0.00200109
$595$	0	0
$596$	−1.20598e46	−1.94884
$597$	− 8.37872e45i	− 1.31705i
$598$	− 1.06764e43i	− 0.00163251i
$599$	2.88158e45	0.428636	0.214318	−	0.976764i	$-0.431247\pi$
$599$	2.88158e45	0.428636	0.214318	+	0.976764i	$0.431247\pi$
$600$	0	0
$601$	−5.17029e45	−0.727924	−0.363962	−	0.931414i	$-0.618576\pi$
$601$	−5.17029e45	−0.727924	−0.363962	+	0.931414i	$0.618576\pi$
$602$	− 6.29907e43i	− 0.00862848i
$603$	6.75853e44i	0.0900776i
$604$	4.95444e45	0.642518
$605$	0	0
$606$	3.05859e43	0.00375597
$607$	6.70496e45i	0.801277i	0.916236	+	0.400639i	$0.131212\pi$
$607$	6.70496e45i	0.801277i	−0.916236	+	0.400639i	$0.868788\pi$
$608$	− 9.52441e43i	− 0.0110772i
$609$	−1.27023e46	−1.43779
$610$	0	0
$611$	−1.74170e46	−1.86764
$612$	3.89085e45i	0.406113i
$613$	− 5.31969e45i	− 0.540491i	−0.962791	−	0.270246i	$-0.912895\pi$
$613$	− 5.31969e45i	− 0.540491i	0.962791	−	0.270246i	$-0.0871049\pi$
$614$	−1.75445e43	−0.00173525
$615$	0	0
$616$	−4.64504e43	−0.00435419
$617$	− 1.86107e46i	− 1.69847i	−0.528013	−	0.849237i	$-0.677063\pi$
$617$	− 1.86107e46i	− 1.69847i	0.528013	−	0.849237i	$-0.322937\pi$
$618$	− 3.63723e43i	− 0.00323192i
$619$	−5.57296e45	−0.482159	−0.241080	−	0.970505i	$-0.577501\pi$
$619$	−5.57296e45	−0.482159	−0.241080	+	0.970505i	$0.577501\pi$
$620$	0	0
$621$	2.06608e45	0.169487
$622$	− 5.99027e42i	0 0.000478526i
$623$	1.41263e46i	1.09894i
$624$	−1.56268e46	−1.18393
$625$	0	0
$626$	6.60178e43	0.00474443
$627$	− 1.58548e45i	− 0.110980i
$628$	1.82031e46i	1.24111i
$629$	−6.33925e45	−0.421019
$630$	0	0
$631$	−3.09333e45	−0.194958	−0.0974792	−	0.995238i	$-0.531078\pi$
$631$	−3.09333e45	−0.194958	−0.0974792	+	0.995238i	$0.531078\pi$
$632$	4.66067e43i	0.00286165i
$633$	4.06923e43i	0.00243417i
$634$	1.12668e44	0.00656642
$635$	0	0
$636$	6.76527e45	0.374320
$637$	− 1.10997e46i	− 0.598426i
$638$	5.43411e43i	0.00285488i
$639$	1.26264e46	0.646422
$640$	0	0
$641$	−9.35057e45	−0.454654	−0.227327	−	0.973819i	$-0.572999\pi$
$641$	−9.35057e45	−0.454654	−0.227327	+	0.973819i	$0.572999\pi$
$642$	− 1.07431e44i	− 0.00509101i
$643$	2.94884e46i	1.36198i	0.732294	+	0.680989i	$0.238450\pi$
$643$	2.94884e46i	1.36198i	−0.732294	+	0.680989i	$0.761550\pi$
$644$	4.09593e45	0.184389
$645$	0	0
$646$	9.13698e43	0.00390810
$647$	− 3.28551e46i	− 1.36988i	−0.728600	−	0.684940i	$-0.759829\pi$
$647$	− 3.28551e46i	− 1.36988i	0.728600	−	0.684940i	$-0.240171\pi$
$648$	1.60079e44i	0.00650651i
$649$	1.28532e46	0.509300
$650$	0	0
$651$	1.65405e46	0.622964
$652$	4.84768e46i	1.78012i
$653$	3.34222e46i	1.19665i	0.801253	+	0.598325i	$0.204167\pi$
$653$	3.34222e46i	1.19665i	−0.801253	+	0.598325i	$0.795833\pi$
$654$	1.07337e44	0.00374728
$655$	0	0
$656$	−1.48605e46	−0.493309
$657$	6.36271e45i	0.205975i
$658$	3.21533e44i	0.0101507i
$659$	−3.13180e46	−0.964238	−0.482119	−	0.876106i	$-0.660133\pi$
$659$	−3.13180e46	−0.964238	−0.482119	+	0.876106i	$0.660133\pi$
$660$	0	0
$661$	4.24878e46	1.24434	0.622172	−	0.782881i	$-0.286251\pi$
$661$	4.24878e46	1.24434	0.622172	+	0.782881i	$0.286251\pi$
$662$	4.30224e44i	0.0122896i
$663$	− 4.49771e46i	− 1.25319i
$664$	−2.77708e44	−0.00754772
$665$	0	0
$666$	4.09435e43	0.00105891
$667$	− 9.58368e45i	− 0.241800i
$668$	2.77190e45i	0.0682284i
$669$	−4.92907e46	−1.18368
$670$	0	0
$671$	−1.72228e46	−0.393716
$672$	8.65521e44i	0.0193057i
$673$	− 7.35045e46i	− 1.59980i	−0.600134	−	0.799900i	$-0.704886\pi$
$673$	− 7.35045e46i	− 1.59980i	0.600134	−	0.799900i	$-0.295114\pi$
$674$	−3.58402e44	−0.00761170
$675$	0	0
$676$	−6.30467e46	−1.27509
$677$	5.34649e46i	1.05525i	0.849477	+	0.527625i	$0.176917\pi$
$677$	5.34649e46i	1.05525i	−0.849477	+	0.527625i	$0.823083\pi$
$678$	7.13869e43i	0.00137508i
$679$	8.02820e46	1.50927
$680$	0	0
$681$	2.53940e46	0.454782
$682$	− 7.07613e43i	− 0.00123695i
$683$	− 2.23782e46i	− 0.381841i	−0.981605	−	0.190921i	$-0.938853\pi$
$683$	− 2.23782e46i	− 0.381841i	0.981605	−	0.190921i	$-0.0611473\pi$
$684$	1.22638e46	0.204268
$685$	0	0
$686$	3.11575e44	0.00494555
$687$	− 5.92197e46i	− 0.917656i
$688$	− 6.95619e46i	− 1.05236i
$689$	4.86973e46	0.719262
$690$	0	0
$691$	1.74443e46	0.245622	0.122811	−	0.992430i	$-0.460809\pi$
$691$	1.74443e46	0.245622	0.122811	+	0.992430i	$0.460809\pi$
$692$	6.25343e46i	0.859741i
$693$	− 8.97164e45i	− 0.120441i
$694$	−3.68821e44	−0.00483487
$695$	0	0
$696$	1.35009e45	0.0168776
$697$	− 4.27713e46i	− 0.522170i
$698$	− 4.48080e44i	− 0.00534246i
$699$	7.62809e46	0.888264
$700$	0	0
$701$	1.34856e47	1.49804	0.749019	−	0.662549i	$-0.230525\pi$
$701$	1.34856e47	1.49804	0.749019	+	0.662549i	$0.230525\pi$
$702$	1.04750e45i	0.0113656i
$703$	1.99811e46i	0.211766i
$704$	−2.56450e46	−0.265493
$705$	0	0
$706$	1.10077e45	0.0108747
$707$	8.44630e46i	0.815166i
$708$	− 1.59663e47i	− 1.50541i
$709$	1.33803e47	1.23254	0.616271	−	0.787535i	$-0.288643\pi$
$709$	1.33803e47	1.23254	0.616271	+	0.787535i	$0.288643\pi$
$710$	0	0
$711$	−9.00182e45	−0.0791557
$712$	− 1.50144e45i	− 0.0129000i
$713$	1.24796e46i	0.104767i
$714$	−8.30314e44	−0.00681117
$715$	0	0
$716$	3.36185e46	0.263338
$717$	− 1.33181e47i	− 1.01947i
$718$	4.11610e44i	0.00307916i
$719$	1.63878e47	1.19811	0.599053	−	0.800710i	$-0.295544\pi$
$719$	1.63878e47	1.19811	0.599053	+	0.800710i	$0.295544\pi$
$720$	0	0
$721$	1.00442e47	0.701430
$722$	7.28291e44i	0.00497097i
$723$	− 4.52940e46i	− 0.302175i
$724$	−2.43052e47	−1.58494
$725$	0	0
$726$	−8.12315e44	−0.00506140
$727$	7.90263e46i	0.481342i	0.970607	+	0.240671i	$0.0773675\pi$
$727$	7.90263e46i	0.481342i	−0.970607	+	0.240671i	$0.922632\pi$
$728$	4.15338e45i	0.0247306i
$729$	−1.77413e47	−1.03272
$730$	0	0
$731$	2.00213e47	1.11392
$732$	2.13943e47i	1.16377i
$733$	5.70441e46i	0.303386i	0.988428	+	0.151693i	$0.0484725\pi$
$733$	5.70441e46i	0.303386i	−0.988428	+	0.151693i	$0.951528\pi$
$734$	1.57403e44	0.000818520 0
$735$	0	0
$736$	−6.53023e44	−0.00324672
$737$	− 1.28225e46i	− 0.0623389i
$738$	2.76248e44i	0.00131332i
$739$	−3.20833e46	−0.149158	−0.0745789	−	0.997215i	$-0.523761\pi$
$739$	−3.20833e46	−0.149158	−0.0745789	+	0.997215i	$0.523761\pi$
$740$	0	0
$741$	−1.41766e47	−0.630335
$742$	− 8.98991e44i	− 0.00390923i
$743$	3.44334e46i	0.146442i	0.997316	+	0.0732208i	$0.0233278\pi$
$743$	3.44334e46i	0.146442i	−0.997316	+	0.0732208i	$0.976672\pi$
$744$	−1.75804e45	−0.00731268
$745$	0	0
$746$	3.43431e45	0.0136662
$747$	− 5.36378e46i	− 0.208776i
$748$	− 7.38185e46i	− 0.281053i
$749$	2.96673e47	1.10491
$750$	0	0
$751$	−2.36045e47	−0.841271	−0.420635	−	0.907230i	$-0.638193\pi$
$751$	−2.36045e47	−0.841271	−0.420635	+	0.907230i	$0.638193\pi$
$752$	3.55075e47i	1.23801i
$753$	2.66949e47i	0.910566i
$754$	4.85893e45	0.0162149
$755$	0	0
$756$	−4.01867e47	−1.28373
$757$	− 1.08268e47i	− 0.338390i	−0.985583	−	0.169195i	$-0.945883\pi$
$757$	− 1.08268e47i	− 0.338390i	0.985583	−	0.169195i	$-0.0541168\pi$
$758$	2.15318e44i	0 0.000658475i
$759$	−1.08705e46	−0.0325282
$760$	0	0
$761$	−3.72392e47	−1.06697	−0.533486	−	0.845809i	$-0.679118\pi$
$761$	−3.72392e47	−1.06697	−0.533486	+	0.845809i	$0.679118\pi$
$762$	7.90012e44i	0.00221502i
$763$	2.96411e47i	0.813280i
$764$	−7.23229e47	−1.94194
$765$	0	0
$766$	−7.85333e44	−0.00201966
$767$	− 1.14927e48i	− 2.89268i
$768$	3.18517e47i	0.784645i
$769$	9.78850e46	0.236011	0.118005	−	0.993013i	$-0.462350\pi$
$769$	9.78850e46	0.236011	0.118005	+	0.993013i	$0.462350\pi$
$770$	0	0
$771$	5.12204e47	1.18317
$772$	1.04704e47i	0.236744i
$773$	− 3.96450e47i	− 0.877458i	−0.898619	−	0.438729i	$-0.855429\pi$
$773$	− 3.96450e47i	− 0.877458i	0.898619	−	0.438729i	$-0.144571\pi$
$774$	−1.29312e45	−0.00280165
$775$	0	0
$776$	−8.53295e45	−0.0177166
$777$	− 1.81576e47i	− 0.369072i
$778$	− 4.52051e45i	− 0.00899547i
$779$	−1.34814e47	−0.262643
$780$	0	0
$781$	−2.39552e47	−0.447361
$782$	− 6.26459e44i	− 0.00114546i
$783$	9.40291e47i	1.68342i
$784$	−2.26286e47	−0.396682
$785$	0	0
$786$	−3.76153e44	−0.000632255 0
$787$	− 5.95539e47i	− 0.980228i	−0.871658	−	0.490114i	$-0.836955\pi$
$787$	− 5.95539e47i	− 0.980228i	0.871658	−	0.490114i	$-0.163045\pi$
$788$	− 6.81406e47i	− 1.09831i
$789$	6.45818e47	1.01939
$790$	0	0
$791$	−1.97135e47	−0.298437
$792$	9.53570e44i	0.00141380i
$793$	1.53999e48i	2.23620i
$794$	−2.94182e45	−0.00418387
$795$	0	0
$796$	−1.22960e48	−1.67764
$797$	2.43995e47i	0.326076i	0.986620	+	0.163038i	$0.0521293\pi$
$797$	2.43995e47i	0.326076i	−0.986620	+	0.163038i	$0.947871\pi$
$798$	2.61712e45i	0.00342591i
$799$	−1.02198e48	−1.31045
$800$	0	0
$801$	2.89995e47	0.356824
$802$	− 4.09935e45i	− 0.00494126i
$803$	− 1.20715e47i	− 0.142546i
$804$	−1.59282e47	−0.184264
$805$	0	0
$806$	−6.32716e45	−0.00702555
$807$	1.08059e48i	1.17556i
$808$	− 8.97733e45i	− 0.00956885i
$809$	4.06571e47	0.424606	0.212303	−	0.977204i	$-0.431904\pi$
$809$	4.06571e47	0.424606	0.212303	+	0.977204i	$0.431904\pi$
$810$	0	0
$811$	1.74453e48	1.74918	0.874591	−	0.484862i	$-0.161130\pi$
$811$	1.74453e48	1.74918	0.874591	+	0.484862i	$0.161130\pi$
$812$	1.86409e48i	1.83144i
$813$	8.69625e47i	0.837216i
$814$	−7.76792e44	−0.000732828 0
$815$	0	0
$816$	−9.16933e47	−0.830711
$817$	− 6.31063e47i	− 0.560285i
$818$	− 1.09872e46i	− 0.00955997i
$819$	−8.02203e47	−0.684069
$820$	0	0
$821$	8.84220e47	0.724267	0.362133	−	0.932126i	$-0.382049\pi$
$821$	8.84220e47	0.724267	0.362133	+	0.932126i	$0.382049\pi$
$822$	− 9.88858e45i	− 0.00793869i
$823$	− 1.96507e48i	− 1.54625i	−0.634251	−	0.773127i	$-0.718691\pi$
$823$	− 1.96507e48i	− 1.54625i	0.634251	−	0.773127i	$-0.281309\pi$
$824$	−1.06757e46	−0.00823375
$825$	0	0
$826$	−2.12165e46	−0.0157218
$827$	− 2.21957e48i	− 1.61223i	−0.591757	−	0.806117i	$-0.701565\pi$
$827$	− 2.21957e48i	− 1.61223i	0.591757	−	0.806117i	$-0.298435\pi$
$828$	− 8.40845e46i	− 0.0598708i
$829$	−7.98020e47	−0.557012	−0.278506	−	0.960435i	$-0.589839\pi$
$829$	−7.98020e47	−0.557012	−0.278506	+	0.960435i	$0.589839\pi$
$830$	0	0
$831$	−9.59889e47	−0.643879
$832$	2.29306e48i	1.50793i
$833$	− 6.51295e47i	− 0.419890i
$834$	6.96388e45	0.00440161
$835$	0	0
$836$	−2.32673e47	−0.141365
$837$	− 1.22442e48i	− 0.729390i
$838$	− 4.40346e45i	− 0.00257198i
$839$	2.69129e48	1.54131	0.770653	−	0.637255i	$-0.219930\pi$
$839$	2.69129e48	1.54131	0.770653	+	0.637255i	$0.219930\pi$
$840$	0	0
$841$	2.54554e48	1.40167
$842$	8.50292e45i	0.00459112i
$843$	− 1.64397e48i	− 0.870442i
$844$	5.97171e45	0.00310062
$845$	0	0
$846$	6.60067e45	0.00329592
$847$	− 2.24321e48i	− 1.09849i
$848$	− 9.92775e47i	− 0.476781i
$849$	3.10265e48	1.46136
$850$	0	0
$851$	1.36996e47	0.0620685
$852$	2.97573e48i	1.32233i
$853$	− 2.54820e46i	− 0.0111064i	−0.999985	−	0.00555321i	$-0.998232\pi$
$853$	− 2.54820e46i	− 0.0111064i	0.999985	−	0.00555321i	$-0.00176765\pi$
$854$	2.84295e46	0.0121538
$855$	0	0
$856$	−3.15325e46	−0.0129700
$857$	− 1.60067e47i	− 0.0645831i	−0.999478	−	0.0322915i	$-0.989719\pi$
$857$	− 1.60067e47i	− 0.0645831i	0.999478	−	0.0322915i	$-0.0102805\pi$
$858$	− 5.51136e45i	− 0.00218131i
$859$	2.01059e48	0.780612	0.390306	−	0.920685i	$-0.372369\pi$
$859$	2.01059e48	0.780612	0.390306	+	0.920685i	$0.372369\pi$
$860$	0	0
$861$	1.22510e48	0.457742
$862$	− 2.11377e46i	− 0.00774797i
$863$	− 1.75008e48i	− 0.629332i	−0.949202	−	0.314666i	$-0.898107\pi$
$863$	− 1.75008e48i	− 0.629332i	0.949202	−	0.314666i	$-0.101893\pi$
$864$	6.40705e46	0.0226038
$865$	0	0
$866$	1.08225e46	0.00367522
$867$	− 2.82996e47i	− 0.0942898i
$868$	− 2.42737e48i	− 0.793524i
$869$	1.70785e47	0.0547803
$870$	0	0
$871$	−1.14653e48	−0.354067
$872$	− 3.15047e46i	− 0.00954671i
$873$	− 1.64809e48i	− 0.490057i
$874$	−1.97457e45	−0.000576149 0
$875$	0	0
$876$	−1.49953e48	−0.421345
$877$	− 6.70977e47i	− 0.185018i	−0.995712	−	0.0925091i	$-0.970511\pi$
$877$	− 6.70977e47i	− 0.185018i	0.995712	−	0.0925091i	$-0.0294887\pi$
$878$	1.96623e46i	0.00532078i
$879$	5.28516e48	1.40359
$880$	0	0
$881$	5.25499e48	1.34422	0.672109	−	0.740452i	$-0.265389\pi$
$881$	5.25499e48	1.34422	0.672109	+	0.740452i	$0.265389\pi$
$882$	4.20654e45i	0.00105607i
$883$	− 3.43775e48i	− 0.847076i	−0.905878	−	0.423538i	$-0.860788\pi$
$883$	− 3.43775e48i	− 0.847076i	0.905878	−	0.423538i	$-0.139212\pi$
$884$	−6.60051e48	−1.59630
$885$	0	0
$886$	−5.27870e46	−0.0122990
$887$	3.38480e48i	0.774092i	0.922060	+	0.387046i	$0.126505\pi$
$887$	3.38480e48i	0.774092i	−0.922060	+	0.387046i	$0.873495\pi$
$888$	1.92992e46i	0.00433236i
$889$	−2.18162e48	−0.480729
$890$	0	0
$891$	5.86594e47	0.124553
$892$	7.23355e48i	1.50776i
$893$	3.22123e48i	0.659132i
$894$	−5.28323e46	−0.0106128
$895$	0	0
$896$	1.69355e47	0.0327882
$897$	9.71991e47i	0.184751i
$898$	− 3.00471e46i	− 0.00560715i
$899$	−5.67956e48	−1.04059
$900$	0	0
$901$	2.85740e48	0.504676
$902$	− 5.24107e45i	0 0.000908892i
$903$	5.73472e48i	0.976483i
$904$	2.09530e46	0.00350321
$905$	0	0
$906$	2.17048e46	0.00349897
$907$	− 8.28291e48i	− 1.31118i	−0.755117	−	0.655590i	$-0.772420\pi$
$907$	− 8.28291e48i	− 1.31118i	0.755117	−	0.655590i	$-0.227580\pi$
$908$	− 3.72664e48i	− 0.579296i
$909$	1.73392e48	0.264683
$910$	0	0
$911$	−2.04653e48	−0.301277	−0.150638	−	0.988589i	$-0.548133\pi$
$911$	−2.04653e48	−0.301277	−0.150638	+	0.988589i	$0.548133\pi$
$912$	2.89014e48i	0.417834i
$913$	1.01763e48i	0.144485i
$914$	−2.80177e46	−0.00390680
$915$	0	0
$916$	−8.69065e48	−1.16890
$917$	− 1.03875e48i	− 0.137220i
$918$	6.14643e46i	0.00797478i
$919$	8.18528e48	1.04310	0.521552	−	0.853219i	$-0.325353\pi$
$919$	8.18528e48	1.04310	0.521552	+	0.853219i	$0.325353\pi$
$920$	0	0
$921$	1.59726e48	0.196378
$922$	3.54352e46i	0.00427932i
$923$	2.14197e49i	2.54088i
$924$	2.11439e48	0.246376
$925$	0	0
$926$	4.89670e46	0.00550582
$927$	− 2.06195e48i	− 0.227753i
$928$	− 2.97196e47i	− 0.0322479i
$929$	−1.84054e48	−0.196194	−0.0980971	−	0.995177i	$-0.531276\pi$
$929$	−1.84054e48	−0.196194	−0.0980971	+	0.995177i	$0.531276\pi$
$930$	0	0
$931$	−2.05286e48	−0.211197
$932$	− 1.11944e49i	− 1.13146i
$933$	5.45359e47i	0.0541546i
$934$	−3.63929e46	−0.00355053
$935$	0	0
$936$	8.52638e46	0.00802996
$937$	− 1.09333e49i	− 1.01169i	−0.862625	−	0.505844i	$-0.831181\pi$
$937$	− 1.09333e49i	− 1.01169i	0.862625	−	0.505844i	$-0.168819\pi$
$938$	2.11659e46i	0.00192437i
$939$	−6.01031e48	−0.536927
$940$	0	0
$941$	−4.25945e48	−0.367388	−0.183694	−	0.982984i	$-0.558805\pi$
$941$	−4.25945e48	−0.367388	−0.183694	+	0.982984i	$0.558805\pi$
$942$	7.97454e46i	0.00675874i
$943$	9.24323e47i	0.0769805i
$944$	−2.34298e49	−1.91748
$945$	0	0
$946$	2.45335e46	0.00193890
$947$	− 6.13570e48i	− 0.476529i	−0.971200	−	0.238265i	$-0.923421\pi$
$947$	− 6.13570e48i	− 0.476529i	0.971200	−	0.238265i	$-0.0765786\pi$
$948$	− 2.12151e48i	− 0.161922i
$949$	−1.07938e49	−0.809622
$950$	0	0
$951$	−1.02574e49	−0.743120
$952$	2.43708e47i	0.0173524i
$953$	1.00078e49i	0.700334i	0.936687	+	0.350167i	$0.113875\pi$
$953$	1.00078e49i	0.700334i	−0.936687	+	0.350167i	$0.886125\pi$
$954$	−1.84552e46	−0.00126932
$955$	0	0
$956$	−1.95447e49	−1.29859
$957$	− 4.94726e48i	− 0.323086i
$958$	9.86018e46i	0.00632928i
$959$	2.73074e49	1.72295
$960$	0	0
$961$	−9.00773e48	−0.549135
$962$	6.94572e46i	0.00416226i
$963$	− 6.09032e48i	− 0.358762i
$964$	−6.64702e48	−0.384907
$965$	0	0
$966$	1.79438e46	0.00100413
$967$	2.67343e49i	1.47072i	0.677674	+	0.735362i	$0.262988\pi$
$967$	2.67343e49i	1.47072i	−0.677674	+	0.735362i	$0.737012\pi$
$968$	2.38425e47i	0.0128946i
$969$	−8.31838e48	−0.442279
$970$	0	0
$971$	−1.33820e49	−0.687708	−0.343854	−	0.939023i	$-0.611732\pi$
$971$	−1.33820e49	−0.687708	−0.343854	+	0.939023i	$0.611732\pi$
$972$	1.42118e49i	0.718053i
$973$	1.92308e49i	0.955291i
$974$	−1.00839e47	−0.00492499
$975$	0	0
$976$	3.13952e49	1.48232
$977$	9.15286e48i	0.424909i	0.977171	+	0.212455i	$0.0681458\pi$
$977$	9.15286e48i	0.424909i	−0.977171	+	0.212455i	$0.931854\pi$
$978$	2.12370e47i	0.00969400i
$979$	−5.50187e48	−0.246943
$980$	0	0
$981$	6.08496e48	0.264070
$982$	− 1.71270e47i	− 0.00730873i
$983$	1.92101e49i	0.806114i	0.915175	+	0.403057i	$0.132052\pi$
$983$	1.92101e49i	0.806114i	−0.915175	+	0.403057i	$0.867948\pi$
$984$	−1.30213e47	−0.00537322
$985$	0	0
$986$	2.85107e47	0.0113773
$987$	− 2.92726e49i	− 1.14876i
$988$	2.08045e49i	0.802913i
$989$	−4.32676e48	−0.164219
$990$	0	0
$991$	1.15219e49	0.422968	0.211484	−	0.977381i	$-0.432170\pi$
$991$	1.15219e49	0.422968	0.211484	+	0.977381i	$0.432170\pi$
$992$	3.87000e47i	0.0139723i
$993$	− 3.91679e49i	− 1.39081i
$994$	3.95425e47	0.0138098
$995$	0	0
$996$	1.26411e49	0.427076
$997$	8.77081e48i	0.291454i	0.989325	+	0.145727i	$0.0465521\pi$
$997$	8.77081e48i	0.291454i	−0.989325	+	0.145727i	$0.953448\pi$
$998$	2.21648e46i	0 0.000724453i
$999$	−1.34412e49	−0.432124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.11		22
5.2	odd	4		25.34.a.e.1.6	yes	11
5.3	odd	4		25.34.a.d.1.6	✓	11
5.4	even	2	inner	25.34.b.d.24.12		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.6	✓	11	5.3	odd	4
25.34.a.e.1.6	yes	11	5.2	odd	4
25.34.b.d.24.11		22	1.1	even	1	trivial
25.34.b.d.24.12		22	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-642.905i q^{2} +5.85306e7i q^{3} +8.58952e9 q^{4} +3.76296e10 q^{6} +1.03914e14i q^{7} -1.10448e13i q^{8} +2.13323e15 q^{9} +O(q^{10})\)	\(q-642.905i q^{2} +5.85306e7i q^{3} +8.58952e9 q^{4} +3.76296e10 q^{6} +1.03914e14i q^{7} -1.10448e13i q^{8} +2.13323e15 q^{9} -4.04723e16 q^{11} +5.02750e17i q^{12} +3.61885e18i q^{13} +6.68070e16 q^{14} +7.37763e19 q^{16} +2.12343e20i q^{17} -1.37147e18i q^{18} +6.69296e20 q^{19} -6.08216e21 q^{21} +2.60199e19i q^{22} -4.58890e21i q^{23} +6.46456e20 q^{24} +2.32658e21 q^{26} +4.50234e23i q^{27} +8.92574e23i q^{28} +2.08845e24 q^{29} -2.71951e24 q^{31} -1.42305e23i q^{32} -2.36887e24i q^{33} +1.36516e23 q^{34} +1.83234e25 q^{36} +2.98538e25i q^{37} -4.30294e23i q^{38} -2.11813e26 q^{39} -2.01426e26 q^{41} +3.91025e24i q^{42} -9.42876e26i q^{43} -3.47638e26 q^{44} -2.95023e24 q^{46} +4.81286e27i q^{47} +4.31817e27i q^{48} -3.06719e27 q^{49} -1.24286e28 q^{51} +3.10842e28i q^{52} -1.34565e28i q^{53} +2.89458e26 q^{54} +1.14771e27 q^{56} +3.91743e28i q^{57} -1.34267e27i q^{58} -3.17580e29 q^{59} +4.25546e29 q^{61} +1.74839e27i q^{62} +2.21673e29i q^{63} +6.33642e29 q^{64} -1.52296e27 q^{66} +3.16821e29i q^{67} +1.82392e30i q^{68} +2.68591e29 q^{69} +5.91891e30 q^{71} -2.35610e28i q^{72} +2.98266e30i q^{73} +1.91932e28 q^{74} +5.74893e30 q^{76} -4.20565e30i q^{77} +1.36176e29i q^{78} -4.21980e30 q^{79} -1.44937e31 q^{81} +1.29498e29i q^{82} -2.51439e31i q^{83} -5.22429e31 q^{84} -6.06179e29 q^{86} +1.22238e32i q^{87} +4.47007e29i q^{88} +1.35942e32 q^{89} -3.76050e32 q^{91} -3.94165e31i q^{92} -1.59175e32i q^{93} +3.09421e30 q^{94} +8.32918e30 q^{96} -7.72579e32i q^{97} +1.97191e30i q^{98} -8.63369e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * q^99

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